What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.?(1 point)
Responses
320 ft.2
320 ft. squared
512 ft.2
512 ft. squared
256 ft.2
256 ft. squared
128 ft.2
To find the surface area of a square pyramid, we need to calculate the area of the base and the area of all four triangular faces and then add them together.
The area of the base of a square pyramid is given by the formula: s^2, where s is the length of the base edge. In this case, the base edge is 8 ft, so the area of the base is 8^2 = 64 ft^2.
To find the area of each triangular face, we can divide the slant height (16 ft) by 2 to get the height of the triangle. Then, we can use the formula for the area of a triangle: (1/2) * base * height. The base of each triangle is equal to the length of the base edge (8 ft), and the height is equal to half of the slant height (16 ft / 2 = 8 ft). So, the area of each triangular face is (1/2) * 8 ft * 8 ft = 32 ft^2.
Since the square pyramid has four triangular faces, the total area of all four faces is 4 * 32 ft^2 = 128 ft^2.
To find the surface area of the square pyramid, we add the area of the base to the area of the four faces: 64 ft^2 + 128 ft^2 = 192 ft^2.
Therefore, the surface area of the square pyramid is 192 ft^2.
A pastry chef is creating a chocolate dessert in the shape of a triangular pyramid. The pyramid has a base of 5 in., the height of the base is 4.3 in., and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid. (1 point)
Responses
58.25 in.2
58.25 in. squared
47.25 in.2
47.25 in. squared
52.25 in.2
52.25 in. squared
55.75 in.2
To find the surface area of a triangular pyramid, we need to calculate the area of the base and the area of the three triangular faces and then add them together.
The area of the base of a pyramid is given by the formula: (1/2) * base * height, where the base is the length of one side of the triangle and the height is the height of the triangle. In this case, the base is 5 in and the height is 4.3 in. So, the area of the base is (1/2) * 5 in * 4.3 in = 10.75 in^2.
To find the area of each triangular face, we can use the formula for the area of a triangle: (1/2) * base * height. The base of each triangle is equal to the base of the pyramid (5 in), and the height is equal to the slant height of the pyramid (6 in). So, the area of each triangular face is (1/2) * 5 in * 6 in = 15 in^2.
Since the triangular pyramid has three triangular faces, the total area of all three faces is 3 * 15 in^2 = 45 in^2.
To find the surface area of the triangular pyramid, we add the area of the base to the area of the three faces: 10.75 in^2 + 45 in^2 = 55.75 in^2.
Therefore, the surface area of the chocolate pyramid is 55.75 in^2.